Physics Based Flexible Tire Model Integrated With LuGre Tire Friction for Transient Braking and Cornering Analysis

Abstract

In transient vehicle maneuvers, structural tire deformation due to the large load transfer causes abrupt change in normal contact pressure and slip distribution over the contact patch, and it has a dominant effect on characterizing the transient braking and cornering forces including the historydependent frictioninduced hysteresis effect. To account for the dynamic coupling of structural tire deformations and the transient tire friction behavior, a physicsbased flexible tire model is developed using the laminated composite shell element based on the absolute nodal coordinate formulation and the distributed parameter LuGre tire friction model. In particular, a numerical procedure to integrate the distributed parameter LuGre tire friction model into the finiteelement based spatial flexible tire model is proposed. To this end, the spatially discretized form of the LuGre tire friction model is derived and integrated into the finiteelement tire model such that change in the normal contact pressure and slip distributions over the contact patch predicted by the deformable tire model enters into the spatially discretized LuGre tire friction model to predict the transient shear contact stress distribution. By doing so, the structural tire deformation and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. The tire model developed is experimentally validated and several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physicsbased flexible tire model developed in this study.